## MeganDarling 3 years ago A food store makes a 11–pound mixture of peanuts, almonds, and raisins. The cost of peanuts is \$1.50 per pound, almonds cost \$3.00 per pound, and raisins cost \$1.50 per pound. The mixture calls for twice as many peanuts as almonds. The total cost of the mixture is \$21.00. How much of each ingredient did the store use? 3 lbs peanuts, 6 lbs almonds, 2 lbs raisins 8 lbs peanuts, 1 lb almonds, 2 lbs raisins 6 lbs peanuts, 3 lbs almonds, 2 lbs raisins 8 lbs peanuts, 2 lbs almonds, 1 lbs raisins

1. jim_thompson5910

Start off by defining variables

2. jim_thompson5910

let x = amount of peanuts (in pounds), y = amount of almonds (in pounds) and z = amount of raisins (in pounds)

3. MeganDarling

okey (:

4. jim_thompson5910

If "A food store makes a 11–pound mixture of peanuts, almonds, and raisins" then what does this mean?

5. MeganDarling

That they add up to 11 pounds haha

6. jim_thompson5910

good, so x y and z add to 11, which means x+y+z = 11

7. jim_thompson5910

that's one equation

8. MeganDarling

so x+y+z=11 :o

9. jim_thompson5910

yes

10. MeganDarling

But then we have to factor in how much they cost..

11. jim_thompson5910

We also know that "The cost of peanuts is \$1.50 per pound, almonds cost \$3.00 per pound, and raisins cost \$1.50 per pound" So x lbs of peanuts cost 1.5x dollars, y lbs of almonds cost 3y dollars, and z lbs of raisins cost 1.5z dollars They total 1.5x + 3y + 1.5z dollars

12. jim_thompson5910

this total cost is given to be \$21 so 1.5x + 3y + 1.5z = 21

13. MeganDarling

so like, 1.50x+3.00y+1.50=21..

14. MeganDarling

15. MeganDarling

1.50z* I meant btw haha. I get that indeed.

16. jim_thompson5910

close, you mean to say 1.50x+3.00y+1.50z=21 but you got it

17. MeganDarling

And don't forget twice the peanuts!

18. jim_thompson5910

19. jim_thompson5910

twice the peanuts as what?

20. MeganDarling

it says, the recipe calls for twice as many peanuts as almonds O.o

21. jim_thompson5910

good, so the equation for that is?

22. MeganDarling

ermm.. I dunno lol.. x(times2y)+y+z=11 O.O I have no idea.

23. jim_thompson5910

not quite

24. MeganDarling

knew it was wrong x.x

25. jim_thompson5910

Amount of peanuts = 2 times (amount of almonds)

26. jim_thompson5910

y = 2 times x or just y = 2x

27. MeganDarling

oh pshh I should have thought of that x.x

28. jim_thompson5910

so you have these 3 equations x+y+z = 11 1.5x + 3y + 1.5z = 21 y = 2x

29. jim_thompson5910

you can use them to solve for x, y and z

30. jim_thompson5910

I'll get you started

31. MeganDarling

Lol I can't because I'm stupid, But smart people definitely can haha

32. jim_thompson5910

x+y+z = 11 x+2x+z = 11 3x+z = 11 --------------------- 1.5x + 3y + 1.5z = 21 1.5x + 3(2x) + 1.5z = 21 1.5x + 6x + 1.5z = 21 7.5x + 1.5z = 21

33. jim_thompson5910

so after plugging in y = 2x, you now have the new system 3x+z = 11 7.5x + 1.5z = 21

34. MeganDarling

O.o That all made absolutely no sense to me but it seems to for you and that's good enough for me

35. jim_thompson5910

where are you lost?

36. jim_thompson5910

I took x+y+z = 11 plugged in y = 2x (ie replaced every 'y' with '2x') to get x+2x+z = 11 then I combined like terms to get 3x+z = 11

37. jim_thompson5910

I did the same with 1.5x + 3y + 1.5z = 21 to get 7.5x + 1.5z = 21

38. MeganDarling

oh okay ! I see now, sorry it's really late and I'm super tired :/

39. jim_thompson5910

so you have 3x+z = 11 7.5x + 1.5z = 21 now

40. jim_thompson5910

solve the first equation for z to get this 3x+z = 11 3x+z - 3x = 11 - 3x z = 11 - 3x

41. MeganDarling

Alrighty

42. jim_thompson5910

Since z = 11 - 3x, you can plug it into the other equation and solve for x 7.5x + 1.5z = 21 7.5x + 1.5(11 - 3x) = 21 Solve for x

43. jim_thompson5910

oh wait, i made a variable mistake...i switched x and y one sec

44. jim_thompson5910

Let me fix real quick

45. MeganDarling

I was thinking that haha x) ..

46. MeganDarling

uhh ? your comment disappeared .. :o

47. jim_thompson5910

it should be x = 2y, not y = 2x so x+y+z = 11 2y+y+z = 11 3y + z = 11 z = 11 - 3y --------------------------- 1.5x + 3y + 1.5z = 21 1.5(2y) + 3y + 1.5z = 21 3y + 3y + 1.5z = 21 6y + 1.5z = 21 =========================== 6y + 1.5z = 21 6y + 1.5(11 - 3y) = 21 Solve that last equation for y

48. jim_thompson5910

sry

49. jim_thompson5910

Solve 6y + 1.5(11 - 3y) = 21 for y

50. MeganDarling

haha it's okay

51. MeganDarling

Aw man I have to go to bed soon I'm dead tired x.x

52. jim_thompson5910

What do you get when you solve that equation for y

53. MeganDarling

ergh I dunno x.x I'm brain dead

54. jim_thompson5910

Then give it a break, get some sleep and you'll tackle it in the morning

55. MeganDarling

Oh no I keep losing connection >.<